Question

Rob had twice as much money as Sam. Then Sam gave Rob 1 quarter, 2 nickels, and 3 pennies. Rob then gave Sam 8 dimes. If they now have the same amount of money, how much money did Rob originally have? (Steps please!)

Answer 1

Let the initial amount that Sam had be x.

Then, since Rob had twice as much as Sam, Rob's money would be 2x.

Now, Sam gave 1 quarter, 2 nickels and 3 pennies to Rob.

Let's convert all of them into pennies.

1 quarter + 2 nickels + 3 pennies = 25 + (2 x 5) + 3

                                                      = 38 pennies

So, Sam's amount is x - 38 and Rob's amount is 2x + 38.

Now, Rob gives 8 dimes to Sam.

8 dimes = 80 pennies.

So, Sam's amount now is x - 38 + 80 = x + 42 and

Rob's amount is 2x + 38 - 80 = 2x - 42

Its given that these two amounts are same.

So,  2x - 42 = x + 42

2x - x = 42 + 42

x = 84

Rob's original amount = 2x = 2(84) = 168 pennies.

                                                         = $1 + 6 dimes + 1 nickel + 3 pennies